Commutants that do not dilate
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- by Douglas N. Clark
- Proc. Amer. Math. Soc. 35 (1972), 483-486
- DOI: https://doi.org/10.1090/S0002-9939-1972-0303313-X
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Abstract:
The Lifting Theorem deals with dilation of the commutant of an operator ${T_1}$ on Hilbert space. In this note, counterexamples are given to generalizations of the theorem involving N commuting operators ${T_1},{T_2}, \cdots ,{T_N}$.References
- Douglas N. Clark, On commuting contractions, J. Math. Anal. Appl. 32 (1970), 590â596. MR 267407, DOI 10.1016/0022-247X(70)90281-7
- Stephen Parrott, Unitary dilations for commuting contractions, Pacific J. Math. 34 (1970), 481â490. MR 268710
- Donald Sarason, Generalized interpolation in $H^{\infty }$, Trans. Amer. Math. Soc. 127 (1967), 179â203. MR 208383, DOI 10.1090/S0002-9947-1967-0208383-8
- BĂ©la Sz.-Nagy and Ciprian FoiaĆ, Commutants de certains opĂ©rateurs, Acta Sci. Math. (Szeged) 29 (1968), 1â17 (French). MR 242011 â, Dilatation des commutants dâopĂ©rateurs, C. R. Acad. Sci. Paris SĂ©r. A-B 266 (1968), A493-A495. MR 38 #5049.
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 483-486
- MSC: Primary 47A15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0303313-X
- MathSciNet review: 0303313